Proof of Entangled Particles being Indetermined

[pinkumbra]

I'm sure this has been asked a million times, but how do we know that entangled particles don't "choose" their states when they're separated? If possible, choose the most basic example. Thanks!

 

[Simon Bridge]

They require very careful experiments to show this - however, the difference is in the statistics and the proof is Bell's inequality. Any experiment that verifies this has demonstrated the effect.

Also see:
https://www.physicsforums.com/showthread.php?t=613582
... and the links in that thread for specific examples.